{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/optimal-path-planning-with-random-breakdowns","title":"Optimal Path-Planning with Random Breakdowns","arxiv_id":"2109.06910","date":"2021-09-14","proceeding":null,"authors":["Marissa Gee","Alexander Vladimirsky"],"abstract":"We propose a model for path-planning based on a single performance metric that accurately accounts for the the potential (spatially inhomogeneous) cost of breakdowns and repairs. These random breakdowns (or system faults) happen at a known, spatially inhomogeneous rate. Our model includes breakdowns of two types: total, which halt all movement until an in-place repair is completed, and partial, after which movement continues in a damaged state toward a repair depot. We use the framework of piecewise-deterministic Markov processes to describe the optimal policy for all starting locations. We also introduce an efficient numerical method that uses hybrid value-policy iterations to solve the resulting system of Hamilton-Jacobi-Bellman PDEs. Our method is illustrated through a series of computational experiments that highlight the dependence of optimal policies on the rate and type of breakdowns, with one of them based on Martian terrain data near Jezero Crater.","url_abs":"https://arxiv.org/abs/2109.06910v3","url_pdf":"https://arxiv.org/pdf/2109.06910v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"optimal-path-planning-with-random-breakdowns","repo_url":"https://github.com/eikonal-equation/random_breakdowns","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}